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The Hubbard Model
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Book Synopsis The Hubbard Model by : Dionys Baeriswyl
Download or read book The Hubbard Model written by Dionys Baeriswyl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).
Book Synopsis The Hubbard Model by : Arianna Montorsi
Download or read book The Hubbard Model written by Arianna Montorsi and published by World Scientific. This book was released on 1992 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers a collection of reprints on the Hubbard Model. The major contributions to the subject since its origin are included, with the aim of providing all scientists working on the model and its applications with easy access to the relevant literature.The book is divided into five parts. The introductory part is concerned with the physical origin and motivations of the model, and contains a collection of mainly historical papers. The remaining four sections are intended to present a coherent scenario of the different approaches to the model solution: exact and rigorous statistical mechanics results; variational methods; perturbative approaches; numerical Quantum Monte Carlo and exact diagonalization studies. Among the applications special emphasis is given to high-Tc superconductivity. Each section is preceded by commentary notes from the editor.
Book Synopsis The One-Dimensional Hubbard Model by : Fabian H. L. Essler
Download or read book The One-Dimensional Hubbard Model written by Fabian H. L. Essler and published by Cambridge University Press. This book was released on 2005-02-07 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.
Book Synopsis Ultracold Atomic Physics by : Hui Zhai
Download or read book Ultracold Atomic Physics written by Hui Zhai and published by Cambridge University Press. This book was released on 2021-02-25 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to ultracold atomic physics combining fundamental theory with discussion of cold atom phenomena and applications.
Book Synopsis Quantum Phase Transitions by : Subir Sachdev
Download or read book Quantum Phase Transitions written by Subir Sachdev and published by Cambridge University Press. This book was released on 2011-04-07 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
Book Synopsis The Hubbard Model by : Mario Rasetti
Download or read book The Hubbard Model written by Mario Rasetti and published by World Scientific. This book was released on 1991-07-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles provides authoritative and up-to-date reviews on the Hubbard Model. It will be useful to graduate students and researchers in the field. Contents:The Phase Diagram of the Hubbard Model (M W Long)Charge and Spin Fluctuations in the Hubbard Model: Fermi Liquid Properties at Low Temperatures (M Lavagna)The t-J and Frustrated Heisenberg Models: A Status Report on Numerical Studies (E Dagotto)The Hubbard-Stratonovich Transformation and the Hubbard Model (S Sorella)SO4 Symmetry in a Hubbard Model (C N Yang & S C Zhang)Mott Transition in an Exactly Solvable K.S.S.H. Model (A Montorsi & M Rasetti)The Hubbard Model: From Small to Large U (D Baeriswyl & W von der Linden)First-Order Metal-Insulator Transition in an Alloy Analogy Approach to the Hubbard Model (M Corrias)Renormalization Group Approach to Quasi-One-Dimensional Conductors (C Bourbonnais & L G Caron) Readership: Physicists and chemists. keywords:
Book Synopsis Hubbard Operators in the Theory of Strongly Correlated Electrons by : S. G. Ovchinnikov
Download or read book Hubbard Operators in the Theory of Strongly Correlated Electrons written by S. G. Ovchinnikov and published by Imperial College Press. This book was released on 2004 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first systematic discourse on a very peculiarapproach to the theory of strongly correlated systems. HubbardX-operators have been known for a long time but have not been widelyused because of their awkward algebra. The book shows that it ispossible to deal with X-operators even in the general multilevel localeigenstate system, and not just in the case of the nondegenerateHubbard model. X-operators provide the natural language for describingquasiparticles in the Hubbard subbands with unusual doping andtemperature-dependent band structures.
Book Synopsis Condensed Matter Physics and Exactly Soluble Models by : Elliott H. Lieb
Download or read book Condensed Matter Physics and Exactly Soluble Models written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.
Book Synopsis Interacting Electrons and Quantum Magnetism by : Assa Auerbach
Download or read book Interacting Electrons and Quantum Magnetism written by Assa Auerbach and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
Book Synopsis Dynamical Mean-Field Theory for Strongly Correlated Materials by : Volodymyr Turkowski
Download or read book Dynamical Mean-Field Theory for Strongly Correlated Materials written by Volodymyr Turkowski and published by Springer Nature. This book was released on 2021-04-22 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that provides a detailed summary of one of the most successful new condensed matter theories - dynamical mean-field theory (DMFT) - in both static and dynamical cases of systems of different sizes. DMFT is one of the most successful approaches to describe the physical properties of systems with strong electron-electron correlations such as bulk materials, multi-layers, surfaces, 2D materials and nanostructures in both metallic and insulating phases. Strongly correlated materials usually include partially-filled localized d- or f-orbitals, and DMFT takes into account crucial for these systems time-resolved interaction between electrons when they “meet” on one atom and occupy one of these orbitals. The First Part of the book covers the general formalism of DMFT as a many-body theory, followed by generalizations of the approach on the cases of finite systems and out-of-equilibrium regime. In the last Chapter of the First Part we discuss generalizations of the approach on the case when the non-local interactions are taken into account. The Second Part of the book covers methodologies of merging DMFT with ab initio static Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) approaches. Such combined DFT+DMFT and DMFT+TDDFT computational techniques allow one to include the effects of strong electron-electron correlations at the accurate ab initio level. These tools can be applied to complex multi-atom multi-orbital systems currently not accessible to DMFT. The book helps broad audiences of students and researchers from the theoretical and computational communities of condensed matter physics, material science, and chemistry to become familiar with this state-of-art approach and to use it for reaching a deeper understanding of the properties of strongly correlated systems and for synthesis of new technologically-important materials.
Book Synopsis Lecture Notes on Electron Correlation and Magnetism by : Patrik Fazekas
Download or read book Lecture Notes on Electron Correlation and Magnetism written by Patrik Fazekas and published by World Scientific. This book was released on 1999 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Graduate students and researchers in condensed matter physics.
Book Synopsis Physics and Mathematics of Quantum Many-Body Systems by : Hal Tasaki
Download or read book Physics and Mathematics of Quantum Many-Body Systems written by Hal Tasaki and published by Springer Nature. This book was released on 2020-05-07 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.
Book Synopsis Condensed Matter Field Theory by : Alexander Altland
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Book Synopsis The Hubbard Model by : Mario Rasetti
Download or read book The Hubbard Model written by Mario Rasetti and published by World Scientific. This book was released on 1991 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles provides authoritative and up-to-date reviews on the Hubbard Model. It will be useful to graduate students and researchers in the field.
Book Synopsis Beautiful Models by : Bill Sutherland
Download or read book Beautiful Models written by Bill Sutherland and published by World Scientific. This book was released on 2004 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Key Features; An original book - not just a collection of reprints - by an expert, and in many cases the originator, in the field; Although most of the important results are derived, the book also discusses in depth the motivation and meaning of these results; The intrinisic beauty of these models and their solution is emphasized throughout the text, in part by unique full-color figures Readership: Advanced undergraduates and graduate students in physics; non-experts interested in exactly solved quantum many-body systems.
Book Synopsis Field Theories of Condensed Matter Physics by : Eduardo Fradkin
Download or read book Field Theories of Condensed Matter Physics written by Eduardo Fradkin and published by Cambridge University Press. This book was released on 2013-02-28 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Book Synopsis A Modern Course in the Quantum Theory of Solids by : Fuxiang Han
Download or read book A Modern Course in the Quantum Theory of Solids written by Fuxiang Han and published by World Scientific. This book was released on 2013 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains advanced subjects in solid state physics with emphasis on the theoretical exposition of various physical phenomena in solids using quantum theory, hence entitled "A modern course in the quantum theory of solids." The use of the adjective "modern" in the title is to reflect the fact that some of the new developments in condensed matter physics have been included in the book. The new developments contained in the book are mainly in experimental methods (inelastic neutron scattering and photoemission spectroscopy), in magnetic properties of solids (the itinerant magnetism, the superexchange, the Hubbard model, and giant and colossal magnetoresistance), and in optical properties of solids (Raman scattering). Besides the new developments, the Green's function method used in many-body physics and the strong-coupling theory of superconductivity are also expounded in great details.
